OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,4,0,-1,4,-4).
FORMULA
G.f.: B(x)^2, where B(x) is the g.f. of A387516.
G.f.: 1/((1-x^3-2*x^4)^2 - 8*x^7).
a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).
MATHEMATICA
Table[Sum[2^(n-3*k)*Binomial[2*k+2, 2*n-6*k+1]/2, {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 02 2025 *)
PROG
(PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+2, 2*n-6*k+1))/2;
(Magma) [&+[2^(n-3*k) * Binomial(2*k+2, 2*n-6*k+1)/2: k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 02 2025
STATUS
approved